If your ship isn't damaged at the start, think about
Diverting power to your engines or guns. The more
guns you have the more powerful the Divert action becomes.

When your ship is damaged, Hold it Together is a
short action to get you through the round, Patch is a
multi round action to get you through the fight.

Overpower is like the Divert action, but spends a
resolve point to affect all three types of systems.

Quick Fix spends a resolve point to remove a
critical condition from a system.

Step Four Piloting Check as pseudo Initiative;

It is not crucial that you win this, (don't burn your ship's computer bonus
on winning here) but losing the piloting check changes your odds in some
actions, and limits your options if you do not have turreted weapons.

If you win your problems are solved move onto Helm
and Gunnery phases.

Step Five Helm Phase

Fly is the basic movement and
Glide is a clumsy half movement for a ship without a
dedicated Pilot.

If you lose initiative and you don't have a turret, you may need to try a
Flyby stunt (DC 15+ 1.5xTier) this gets one arc of
your ship's weapons to attack at close 1 hex range. If your weapons are all
concentrated in one arc this might be desireable just to get your normal shots
off at close range if you only have short range weapons.

If you have weapons all over, this still gives you a chance to get some
shots in with your best weapons to your enemy's weak spot (pick any quadrant
you want).

If you have a turret, pick any other arc of weapons to fire from the Flyby
attack and then also use the turret during the Gunnery phase along with any
other weapon arcs pointing at the target when Helm Phase is over.

If the enemy is more manueverable than you

Manuever and Audacious
Gambit both reduce your turn rate.

The Flip and Burn stunt (DC 15+ 1.5xTier) was
handy with a ship chasing my aft quadrant, he finally lost a piloting check for
initiative and I could open up with my forward guns on him. The clumsiness of
my ship meant turning normally would be a drawn out ordeal.

If you like where you're at, but not where you're facing, or have an enemy
that's so much more maneuverable than you? Turn in
Place might be your answer. It's handy for getting your best guns
or shields in the enemy's face.

If you have no special problems and nothing else looks attractive, use the
Evade stunt (DC 10+ 1.5xTier) this gives you +2 to AC
and TL for the rest of the turn while letting you move normally.

If the enemy is faster than you

Full Power is a thing to try if your Fighter
doesn't have an Engineer or Divert power to Engines
isn't enough.

Other stunts

Barrel Roll helps you get different quadrant guns
and shields into a fight if some of your guns or shields are damaged.

Back Off, I haven't been in a situation to need
it, but I'm certain it'll come up eventually. The Know Direction guys used it
to create space between their craft and a gnarl of other ships. Possibly useful
if turning would move you through other ships hexes.

Slide, I haven't been in a situation to need it,
but I'm certain it'll come up eventually.

Captain Actions

Encourage, Captain grants aid another to one
crewman for one action.

Demand, once per character per combat, the Captain
may grant a +4 bonus to one action.

Taunt, enemy ship takes -2(-4) to their actions
that phase (engineering/helm/gunnery) for the next 1d4 rounds.

Orders, spend a resolve point grant a crew member
another action.

Moving Speech, spend a resolve point to grant your
crew advantage for the rest of the phase.

Science Officer Actions

Scan tells you about enemy ships, best used as
early as possible before Science needs to balance shield points or gunnery
related actions.

Balance, you can move shield points around to keep
any one arc from becoming a weak spot.

Target System broadens your weapon's crit range
and affects the targeted system if a gunner scores a crit on the targeted
ship.

Lock On, spend a resolve point for the Science
Officer to grant aid another to all ship's gunnery checks on one target ship
for the rest of the round. If you only have one Gunner and one gun, the Captain
is better off performing an Encourage or Demand action directly on the
gunner.

Improve Countermeasures, spend a resolve point to
put disadvantage on a targeted ship's gunners.

It seems odd to me that the Science Officer doesn't have a basic aid another
for the gunner, while it would overlap a bit with the Captain's Encourage
action, the Captain has Pilots and Engineers to worry about as well.

Step Six Gunnery Phase

Shoot is the "I swing my sword" of Starship
combat, normal use, best odds of hitting.

If you don't have enough Gunners

Snap Shot, a minor action for Pilots that are
necessarily the only Gunner in a one seater or anyone in an undermanned
ship.

Fire at Will helps if you have more enemies and
guns than gunners.

Other actions

Broadside spend a resolve point for a bigger Fire
at Will, best for undermanned ships.

Precise Targeting, spend a resolve point to
guarantee a critical on an enemy with shields already down.